Maharashtra HSC Workshop Science & Calculation flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Vernier least count

Least count equals one main-scale division minus one vernier-scale division. For a 1 mm main scale and 50 vernier divisions, LC = 1 − 0.98 = 0.02 mm.

Micrometer least count

Least count equals screw pitch divided by the number of thimble divisions. A 0.5 mm pitch with 50 thimble divisions gives 0.01 mm per division.

Zero error correction

If the vernier zero lies right of the main-scale zero, the reading is too large, so subtract the zero error. If it lies left, add the error.

Density formula

Density equals mass divided by volume, ρ = m/V. Rearranged, mass equals density times volume. Keep units consistent: kg with m³ and kg/m³, or g with cm³ and g/cm³.

Mass of round bar

Mass equals π/4 times diameter squared times length times density. With d in mm and L in m for steel at 7850 kg/m³, mass in kg is about 0.006165 d²L.

Cylinder volume

Volume of a cylinder equals π times radius squared times length, or πd²L/4. It gives the volume of a round bar or of metal removed in a boring operation.

Hollow tube volume

Volume of a hollow cylinder equals πL(D² − d²)/4, where D is outside diameter, d is bore diameter and L is length. Multiply by density to obtain mass.

Newton and kilogram-force

One newton is the force giving 1 kg an acceleration of 1 m/s². One kilogram-force equals 9.81 N, so 1 kgf/mm² equals 9.81 N/mm² or 9.81 MPa.

Inch to millimetre

One inch equals exactly 25.4 mm, so multiply inches by 25.4 to get millimetres and divide millimetres by 25.4 to get inches. One mil is 0.0254 mm.

Kilowatt-hour

One kilowatt-hour equals 3.6 megajoules, the energy used by a 1 kW load running for one hour. Energy in kWh equals power in kW times time in hours.

Percentage error

Percentage error equals the absolute difference between measured and true value, divided by the true value, multiplied by 100. It quantifies measurement accuracy.

Casting shrinkage allowance

Pattern size equals finished size multiplied by one plus the shrinkage fraction. A 200 mm casting with 5% shrinkage needs a 210 mm pattern.

Drawing scale conversion

For a reducing scale 1:5, actual length equals drawing length times 5. For an enlarging scale 5:1, actual length equals drawing length divided by 5.

Cutting speed formula

Cutting speed in metres per minute equals π times diameter in mm times rpm divided by 1000. Rearranged, rpm equals 1000V divided by πD.

Turning machining time

Machining time in minutes equals travel length divided by feed per revolution times rpm. Travel length includes approach and overtravel, usually 2 to 5 mm at each end.

Drilling time formula

Drilling time equals length plus 0.3 times drill diameter, divided by feed per revolution times rpm. The 0.3d term accounts for the drill point approach.

Milling table feed

Table feed in mm/min equals feed per tooth times number of teeth times rpm. Machining time equals length of cut divided by table feed.

Depth of cut in turning

Depth of cut equals the difference between original and machined diameter divided by two, because the diameter reduces by twice the depth on each pass.

Taper ratio and percent

Taper equals (D − d)/L. Expressed as a percentage, multiply by 100. Taper is often stated as 1 in n, where n equals L/(D − d).

Taper half angle

The half angle satisfies tan(θ/2) = (D − d)/(2L). The compound slide is swivelled to this half angle for taper turning between centres.

Tap drill size metric

For a metric thread, tap drill diameter is approximately major diameter minus pitch. For M10 × 1.5 the tap drill is about 8.5 mm.

Gear module

Module equals pitch diameter divided by number of teeth, m = d/T. Circular pitch equals πm, addendum equals m and dedendum equals 1.25m.

Gear ratio

Gear ratio equals teeth on driven gear divided by teeth on driver, which also equals driver speed divided by driven speed. Compound trains multiply stage ratios.

Ohm's law and power

Voltage equals current times resistance. Power equals voltage times current, also current squared times resistance, or voltage squared divided by resistance.

Three-phase power

Three-phase power equals √3 times line voltage times line current times power factor. For a 415 V motor at 10 A and 0.85 power factor, power is about 6.1 kW.

Synchronous speed

Synchronous speed in rpm equals 120 times supply frequency divided by the number of poles. A 4-pole motor on 50 Hz runs at 1500 rpm synchronously.

Machine hour rate

Machine hour rate is the cost of running a machine for one hour, covering depreciation, power, maintenance, consumables and floor area. Multiply by machining hours for cost.

Profit on selling price

When profit is a percentage of selling price, selling price equals cost divided by one minus the profit fraction. A 20% profit on price gives cost/0.8.

Break-even quantity

Break-even quantity equals fixed cost divided by selling price per unit minus variable cost per unit. Above this quantity the product makes a profit.

Bearing life L10

Basic rating life L10 equals dynamic capacity divided by equivalent load, cubed, times one million revolutions. It is the life reached by 90% of identical bearings.

Fan affinity laws

For a fan or pump, flow varies with speed, head with speed squared and power with speed cubed. A 10% speed reduction cuts power by about 27%.

Lockout tagout

Isolate the energy source, apply a personal lock and tag, then try to start the machine to confirm zero energy before beginning maintenance work.